Properties and Design of the Phase-Controlled Oscillator with a Sawtooth Comparator

569 569 571 572 572 573 577 577 579 581 581 585 587 588 589 590 593 594 594 595 595 597 599 600 600 600 602 The phase-controlled oscillator (see Fig. 1), otherwise known as the phase-locked oscillator, is often used to produce a signal whose frequency and phase are controlled by an input signal. The literature1'2'3 on the subject assumes that the phase comparator, which is the error detector of the loop, produces an output which is proportional to the sine of the phase difference. This paper considers the case of the sawtooth comparator, whose output is a linear function of the phase difference over a periodic range (see Fig. 2a). Because of this linearity, the sawtooth comparator is superior in operation to the sinusoidal comparator for some applications. In general, the sinusoidal comparator is simpler and cheaper, but in applications involving digital signals, the two are comparable in cost and complexity. The purpose of this paper is to present a comprehensive survey of many properties of the phase-controlled oscillator, relating to many different applications. We have drawn heavily on the literature, modifying the analysis to make it apply to the sawtooth comparator. In addition, there is new theoretical material on the effect of fast jitter and noise. New results derived by A. J. Goldstein in a companion paper4 are presented in an abbreviated form, more suitable for design.